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How to rearrange equations properly ?

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“What positive becomes negative and vice versa” is a terrible way to look at it.

You want to get y on its own with everything else on the other side, so start by getting (-5y) on its own. What do you need to do to do that?
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it says that y = mx + b, so y is alone, to make y alone, move 6x to the other side by subtracting it from both sides

-5y = 15 - 6x

its almost y = mx + b, except for the fact that y has a coefficient, so let's try dividing by it?

-5/-5 y = 15/-5 - 6/-5 x

y = -3 + 6x/5

or y = 6/5 x -3
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>"6x-5y=15"

Subtract 6x from both sides:
-5y=-6x+15

Divide both sides by -5:

y=6/5x-15/5

Simplify:

y=6/5x-3

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